Talk by Urs Koster, Dept. of Computer Science, University of Helsinki; given to the Redwood Center for Theoretical Neuroscience on March 5, 2009 at UC Berkeley.
Note: Slides for this talk (PDF format) can be downloaded by clicking on the "All Files" link on the left.
Abstract: We present a novel extension to Independent Component Analysis (ICA), where the data is generated as the product of two submodels, each of which follow an ICA model, and which combine in a horizontal fashion. This is in contrast to previous nonlinear extensions to ICA which were based on a hierarchy of layers. We apply the product model to natural image patches and report the emergence of localized masks in the additional network layer, while the Gabor features that are obtained in the primary layer change their tuning properties and become less localized. As an interpretation we suggest that the model learns to separate the localization of image features from other properties, since identity and position of a feature are plausibly independent. We also show that the horizontal model can be interpreted as an overcomplete model where the features are no longer independent.